Matching of corresponding branchpoints between two human airway trees, as well as assigning anatomical names to the segments and branchpoints of the human airway tree, are of significant interest for clinical applications and physiological studies. In the past, these tasks were often performed manually due to the lack of automated algorithms that can tolerate false branches and anatomical variability typical for in vivo trees. In this paper, we present algorithms that perform both matching of branchpoints and anatomical labeling of in vivo trees without any human intervention and within a short computing time. No hand-pruning of false branches is required. The results from the automated methods show a high degree of accuracy when validated against reference data provided by human experts. 92.9% of the verifiable branchpoint matches found by the computer agree with experts' results. For anatomical labeling, 97.1% of the automatically assigned segment labels were found to be correct.